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You searched for +publisher:"University of Colorado" +contributor:("Edd V. Taylor"). Showing records 1 – 3 of 3 total matches.

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University of Colorado

1. Miller, Susan Beth. Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities.

Degree: PhD, 2017, University of Colorado

This study investigates instructional moves by teachers in mathematics classrooms in which technology-based activities (i.e., student-oriented simulations) and features of those simulations influence classroom practices. Four teachers were studied over the course of a year as an exploratory study to build interpretive cases that described instructional practices in technology-based lessons. Teachers developed lessons using PhET simulations designed to support algebraic reasoning. Data sources included teachers’ process of selecting and designing lessons, observations of teachers’ non-technology and technology-based mathematical activities, and teacher interviews and reflections. This work was based on a conceptual framework blending the ideas of Mathematical Tasks (Stein, Smith, Henningsen, & Silver, 1998), Mathematical Pedagogical Content Knowledge (Ball, Thames, & Phelps, 2008), and Technological Pedagogical Content Knowledge (Mishra & Koehler, 2006), in which teachers’ instructional practices are determined by teachers’ mathematical pedagogical content knowledge, task selection and design, and use of technology. Results indicated that teachers see simulations as having significant benefits in the classroom. Teachers leveraged these opportunities by increasing class discussions, engaging in higher levels of thinking and reasoning, and focusing on mathematical representations. When teachers used simulations, the teachers spent less time in direct instruction, focused more on the mathematics, and focused more on investigations rather than drill-oriented tasks. Technology in the classroom, however, was problematic for some teachers. The very nature of students working independently with their own devices meant that student-student interactions decreased in some lessons. Furthermore, teachers’ discomfort in managing technology seems to limit ongoing use. Specific features of the simulations that prompted instructional moves included the ability to support conceptual understanding and build student engagement. Simulations also provided a ‘low floor, high ceiling,’ supporting differentiation, and a dynamic responsiveness, facilitating connections between representations. On the other hand, teachers raised concerns that some features of the simulation could do the math for the students. Furthermore, the perception of simulations as being a game may impact how and when simulations are used. The emergent use of technology in math classrooms is under-supported. For simulations to be used in a more extensive fashion in mathematics classes, professional development and curricular materials are needed to support implementation. Advisors/Committee Members: David C. Webb, Ben Shapiro, Edd V. Taylor, Daniel Liston, Joseph Polman.

Subjects/Keywords: curriculum and instruction; instructional practices; mathematics; simulations; teacher education; technology; Curriculum and Instruction; Science and Mathematics Education; Teacher Education and Professional Development

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Miller, S. B. (2017). Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/educ_gradetds/114

Chicago Manual of Style (16th Edition):

Miller, Susan Beth. “Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities.” 2017. Doctoral Dissertation, University of Colorado. Accessed December 04, 2020. https://scholar.colorado.edu/educ_gradetds/114.

MLA Handbook (7th Edition):

Miller, Susan Beth. “Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities.” 2017. Web. 04 Dec 2020.

Vancouver:

Miller SB. Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities. [Internet] [Doctoral dissertation]. University of Colorado; 2017. [cited 2020 Dec 04]. Available from: https://scholar.colorado.edu/educ_gradetds/114.

Council of Science Editors:

Miller SB. Teachers’ Use of Instructional Moves During Technology-Based Mathematical Activities. [Doctoral Dissertation]. University of Colorado; 2017. Available from: https://scholar.colorado.edu/educ_gradetds/114


University of Colorado

2. Johnson, Raymond. Designing for Consensus and the Standards for Mathematical Practice.

Degree: PhD, 2018, University of Colorado

This design research study examined how professional development in the context of a research practice partnership developed Algebra 1 teachers’ collective understanding of the eight Standards for Mathematical Practice (SMPs), part of the Common Core State Standards. Over two years, 15 teachers participated in a task analysis routine that included the alignment of mathematical tasks to the SMPs. Group consensus of these task ratings were analyzed quantitatively using Randolph’s kappa, along with a measure of individual contributions to consensus that was based on calculations of pairwise agreement. Task rating discussions, which targeted disagreement in the task ratings, were analyzed qualitatively using a grounded theory approach. The analyses revealed that consensus for SMP alignment decisions increased over time. Practice 4, <i>model with mathematics</i>, was the only practice for which there was a strong consensus that tasks were aligned to a practice. When alignment to SMPs was correlated with task ratings for cognitive demand, a positive correlation existed between demand and practices one through four, but no correlation existed between demand and practices five through eight. Examination of individual raters’ contributions to SMP alignments showed differences in the use of content knowledge, use of standards definitions, and attention to alignment criteria. Teachers who attended most to the alignment criteria scored highest in their individual contributions to consensus. These findings add to Brown’s theories of <i>design capacity for enactment</i> and <i>pedagogical design capacity</i> (2002, 2009) by arguing that curriculum alignment to academic standards is a process of perceiving affordances in curricular materials, and that the process necessarily relies on consensus interpretations of standards and socially developed criteria for alignment. The implications of this study suggest that task analysis is useful, but not sufficient for developing teachers’ understanding of the SMPs, and that the quantitative methods employed in the analysis of this study could have utility as a formative measure in other professional development and research. Advisors/Committee Members: David C. Webb, Daniel Liston, William R. Penuel, Tamara Sumner, Edd V. Taylor.

Subjects/Keywords: academic standards; design research; pedagogical design capacity; professional development; standards for mathematical practice; standards implementation; Science and Mathematics Education; Teacher Education and Professional Development

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Johnson, R. (2018). Designing for Consensus and the Standards for Mathematical Practice. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/educ_gradetds/121

Chicago Manual of Style (16th Edition):

Johnson, Raymond. “Designing for Consensus and the Standards for Mathematical Practice.” 2018. Doctoral Dissertation, University of Colorado. Accessed December 04, 2020. https://scholar.colorado.edu/educ_gradetds/121.

MLA Handbook (7th Edition):

Johnson, Raymond. “Designing for Consensus and the Standards for Mathematical Practice.” 2018. Web. 04 Dec 2020.

Vancouver:

Johnson R. Designing for Consensus and the Standards for Mathematical Practice. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2020 Dec 04]. Available from: https://scholar.colorado.edu/educ_gradetds/121.

Council of Science Editors:

Johnson R. Designing for Consensus and the Standards for Mathematical Practice. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/educ_gradetds/121


University of Colorado

3. Grover, Ryan. Student Conceptions of Functions: How Undergraduate Mathematics Students Understand and Perceive Functions.

Degree: PhD, Education, 2015, University of Colorado

Functions are an integral element in mathematics. They are essential from secondary mathematics, where students first learn the definition, all the way through graduate school, where students use them in their dissertations, and beyond. Yet, at a time in which more content is being introduced earlier into students’ mathematical experiences, less time is spent with the fundamental concepts of functions. As a result, many students enter undergraduate mathematics with only a procedural understanding despite our expectations for deeper comprehension. This study, therefore, explored the disconnect observed between students’ use of functions procedurally and how they demonstrate their understanding of functions. Using a mixed methods approach of surveys and interviews, students enrolled in a variety of first semester calculus courses (including Business Calc and Bio Calc), Calculus II, and Discrete Math responded to prompts about mathematics and functions and solved problems involving functions and related applications. After examining students’ perceptions, various tasks and interview techniques were used to assess their understanding of functions, including the use of different function representations and more formal, generalizable statements. This study found that students in contextually-driven Calculus I courses tend to focus less on the generalizability of their statements, but they did show evidence of forming connections between various mathematical ideas. Additionally, there is a relationship that students who demonstrated evidence of both generalizability and forming connections also tended to fluently switch between function representations, which often exhibits a higher level of understanding. Advisors/Committee Members: David C. Webb, Erin M. Furtak, Joseph Polman, Eric Stade, Edd V. Taylor.

Subjects/Keywords: Mathematics Education; Postsecondary Education; Higher Education; Science and Mathematics Education

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Grover, R. (2015). Student Conceptions of Functions: How Undergraduate Mathematics Students Understand and Perceive Functions. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/educ_gradetds/80

Chicago Manual of Style (16th Edition):

Grover, Ryan. “Student Conceptions of Functions: How Undergraduate Mathematics Students Understand and Perceive Functions.” 2015. Doctoral Dissertation, University of Colorado. Accessed December 04, 2020. https://scholar.colorado.edu/educ_gradetds/80.

MLA Handbook (7th Edition):

Grover, Ryan. “Student Conceptions of Functions: How Undergraduate Mathematics Students Understand and Perceive Functions.” 2015. Web. 04 Dec 2020.

Vancouver:

Grover R. Student Conceptions of Functions: How Undergraduate Mathematics Students Understand and Perceive Functions. [Internet] [Doctoral dissertation]. University of Colorado; 2015. [cited 2020 Dec 04]. Available from: https://scholar.colorado.edu/educ_gradetds/80.

Council of Science Editors:

Grover R. Student Conceptions of Functions: How Undergraduate Mathematics Students Understand and Perceive Functions. [Doctoral Dissertation]. University of Colorado; 2015. Available from: https://scholar.colorado.edu/educ_gradetds/80

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